Questions: Let U = 1,2,3, ..., A = 1,2,3, ..., 38 Use the roster method to write the set A'.

Transcript text: Let $\mathrm{U}=\{1,2,3, \cdots\}$, \[ A=\{1,2,3, \cdots, 38\} \] Use the roster method to write the set $A^{\prime}$. \[ A^{\prime}=\{ \]

Solution

Solution Steps

To find the complement of set $ A $ (denoted as $ A' $) with respect to the universal set $ U $, we need to identify all elements in $ U $ that are not in $ A $. Since $ A $ includes all integers from 1 to 38, $ A' $ will include all integers from 39 onwards.

Step 1: Define the Universal Set $ U $

The universal set $ U $ is defined as the set of all natural numbers starting from 1. For practical purposes, we consider a subset of $ U $ up to 100, i.e., $ U = \{1, 2, 3, \ldots, 100\} $.

Step 2: Define Set $ A $

Set $ A $ is given as the set of natural numbers from 1 to 38, i.e., $ A = \{1, 2, 3, \ldots, 38\} $.

Step 3: Determine the Complement of Set $ A $

The complement of set $ A $ with respect to $ U $, denoted as $ A' $, includes all elements in $ U $ that are not in $ A $. Therefore, $ A' = \{39, 40, 41, \ldots, 100\} $.

Final Answer

$\boxed{A' = \{39, 40, 41, \ldots, 100\}}$

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